Okay hold on, this sounds like a whole load of bullshit to me.
“Geometric equations predict the dimensions of DNA’s structure.”
No, they match the dimensions of DNA’s structure. The argument is circular; of course pentagons would be able to match the helical structure, because your initial assumption was that the structure is helical.
"The pentagonal geometry … establishes why there should be consistently ten bases contained within a single turn of the helix."
That’s cool and all, but it misses the entire underlying reason. The van der Waals diameter of a carbon atom (and consequently the thickness of a base) is 3.4 angstroms, whereas the distance between the glycosidic bonds between nucleotides in the backbond is 6 angstroms. The bases of DNA are hydrophobic on the flat faces and want to be in as close contact as possible (the so-called “hydrophobic interaction”). There are 10.5 base pairs per turn because at that angle of twisting, the bases are in direct contact with each other, maximizing the “hydrophobic interaction”.
"Both the hollow centre and side-by-side structural formation ensure instant access at any point within the helix."
Yes, but once again this completely ignores the underlying chemistry. A hollow center means that your bases are exposed to water. If you’ve taken an ochem class, then you’ve likely discussed the relevant intermolecular forces that govern the behavior between hydrophobic substances and water. Water would much prefer to make hydrogen bonds with itself than to lose out by interacting with the bases; remember, the formation of bonds is always exothermic. Exposed bases means you have water that isn’t making as many hydrogen bonds as it can, increasing the energy of the entire system.
"This would permit the DNA (even circular) to open and close during its replication functions without entangling itself."
So there’s a family of enzymes called topoisomerases (they’re incredibly intriguing enzymes with really cool mechanisms!) that untangle the DNA as it replicates. DNA does not tangle when replicating; the consequences of that would be the entire cell cycle grinding to a halt because replication can’t be completed.
"The modification to the base pairing would appear to be able to exist in either the enol or keto formations."
I simply can’t with this statement. There are so many things wrong here. Bases generally exist in the keto/amino form rather than the enol/imino form because they’re more thermodynamically stable; the amino form of adenine is favored over the imino form by a factor of 10,000. But more important is that the enol/imino forms are ambiguous when it comes to replicating.
DNA is based on the ability to replicate to make an exact copy of itself, and that relies on the hydrogen bonding capabilities of each base. Think of it as how puzzle pieces can fit together. A and T fit together, as do G and C. But if your adenine goes from the keto form to the enol form, all of a sudden, it can’t fit with T anymore. It’s become a good pairing candidate for C instead—which means you now have an error in replication. Your modification to the base pairing essentially breaks the entire concept of base pairing as it stands.
"… it is the geometry of the basepair molecules themselves that are ultimately responsible for the formation of the helix."
Again, completely wrong. Base pairing is necessary for correct replication, but they are not the driving force in the helix formation. Hydrogen bonds are extremely weak; if they weren’t, water wouldn’t be a liquid at room temperature—it’d be a solid! The reason why DNA helix formation is favorable is because of the whole “hydrophobic interaction” thing as mentioned before.
If you look up and read the actual article, you’ll see even more evidence against this person’s proposal. They suggest that the ribose phosphate backbone isn’t held together by covalent bonds at all, but with hydrogen bonds; even more insane is their suggestion that the bases aren’t covalently attached to the backbone covalently at all. Figure 5 shows hydrogen bonding occuring through N9 of guanine, which is patently impossible since N9 is where guanidine is covalently bound to ribose.
The issue here is that the person is blindly applying math to science, without considering the existing physical limitations already in place. Math might be a powerful tool in explaining the world, but it’s completely meaningless if you use it without looking at the context.
Also, probably the most damning evidence that what we have is accurate is the fact that we have crystal structures of DNA showing the positions of non-hydrogen atoms, and these crystal structures are nothing at all like what this person’s proposed. Checkmate.